Lesson 4.8 - Least Common Multiple
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Five-Minute Check (over Lesson 4–7) Main Idea and Vocabulary Example 1:Find the LCM Example 2:Find the LCM Example 3:Solve a Problem Using the LCM
• Find the least common multiple of two or more numbers.
• multiple • least common multiple (LCM)
Find the LCM Find the LCM of 4 and 6. Method 1 List the nonzero multiples. multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, . . . multiples of 6: 6, 12, 18, 24, 30, 36, . . . Notice that 12, 24, . . ., are common multiples. The least of these is 12, so, the LCM of 4 and 6 is 12.
Find the LCM Method 2 Use Chinese Math
Answer: The LCM of 4 and 6 is 12.
Find the Greatest Common Factor Method 2 Use Chinese Math. Write the two numbers side by side. Look for a common factor. Divide both numbers by that common factor. Look for a common factor between the two quotients, repeat until there are no more common factors.
7
28
42
2
14
6
7
3
7 is a common factor divide both numbers by 7. 2 is a common factor divide both numbers by 2.
The LCM is the product of the common factors and the uncommon factors.
The greatest common factor or GCF is 2 ● 7 ● 7● 3 or 294.
Answer: 294
Find the LCM of 8 and 12. C. 24
0% D
A B C 0% D C
0% B
A
0%
1. 2. 3. 4.
Find the LCM Find the LCM of 4 and 15. Write the prime factorization. 4 = 2 ● 2 or 22 15 = 3 ● 5 The prime factors of 4 and 15 are 2, 3, and 5. Multiply the greatest power of 2, 3, and 5. 22 ● 3 ● 5 = 60 Answer: The LCM of 4 and 15 is 60.
Find the LCM of 6 and 14. D. 42
0% D
A B C 0% D C
0% B
A
0%
1. 2. 3. 4.
WORK On an assembly line, machine A must be oiled every 18 minutes, machine B every 24 minutes, and machine C every 48 minutes. If all three machines are turned on at the same time, in how many minutes will all three machines need to be oiled at the same time? First, find the LCM of 18, 24, and 48. 18 = 2 × 32 24 = 23 × 3 48 = 24 × 3 LCM: 24 × 32 = 144
Answer: So, all three machines will need to be oiled at the same time in 144 minutes.
LIGHTS Brenda put up three different strands of decorative blinking lights. The first strand blinks every 6 seconds while the second strand blinks every 8 seconds. The third strand blinks every 4 seconds. If all strands blink at the same time, in how many seconds will they again blink at the same time? D. 24 s 1. 2. 3. 4.
0% D
0% C
0% B
A
0%
A B C D
End of the Lesson
Homework – Pg 213, # 8-29 all
Five-Minute Check (over Lesson 4–7) Image Bank Math Tools
Percents Prime Factorization
(over Lesson 4-7)
Write 13.7% as a decimal. B. 0.137
0% D
A B C 0% D C
0% B
A
0%
1. 2. 3. 4.
(over Lesson 4-7)
D. 0.0725
0% D
A B C 0% D C
0% B
A
0%
1. 2. 3. 4.
(over Lesson 4-7)
Write 0.183 as a percent. B. 18.3%
0% D
A B C 0% D C
0% B
A
0%
1. 2. 3. 4.
(over Lesson 4-7)
Write 0.07 as a percent. C. 7%
0% D
A B C 0% D C
0% B
A
0%
1. 2. 3. 4.
(over Lesson 4-7)
Assuming every student placed a vote, if 0.83 of the student body voted for Afsheen and 0.17 voted for Neal, what percent of the student body voted for Neal? A. 17% A B C 0% D D
C
0% B
A
0%
1. 2. 3. 0% 4.
(over Lesson 4-7)
What is
% written as a decimal?
A. 0.32 B. 3.2 A B C 0% D
0% D
A
D. 0.325
0% B
0%
1. 2. 3. 4.
C
C.
• Find the least common multiple of two or more numbers.
• multiple • least common multiple (LCM)
Find the LCM Find the LCM of 4 and 6. Method 1 List the nonzero multiples. multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, . . . multiples of 6: 6, 12, 18, 24, 30, 36, . . . Notice that 12, 24, . . ., are common multiples. The least of these is 12, so, the LCM of 4 and 6 is 12.
Find the LCM Method 2 Use Chinese Math
Answer: The LCM of 4 and 6 is 12.
Find the Greatest Common Factor Method 2 Use Chinese Math. Write the two numbers side by side. Look for a common factor. Divide both numbers by that common factor. Look for a common factor between the two quotients, repeat until there are no more common factors.
7
28
42
2
14
6
7
3
7 is a common factor divide both numbers by 7. 2 is a common factor divide both numbers by 2.
The LCM is the product of the common factors and the uncommon factors.
The greatest common factor or GCF is 2 ● 7 ● 7● 3 or 294.
Answer: 294
Find the LCM of 8 and 12. C. 24
0% D
A B C 0% D C
0% B
A
0%
1. 2. 3. 4.
Find the LCM Find the LCM of 4 and 15. Write the prime factorization. 4 = 2 ● 2 or 22 15 = 3 ● 5 The prime factors of 4 and 15 are 2, 3, and 5. Multiply the greatest power of 2, 3, and 5. 22 ● 3 ● 5 = 60 Answer: The LCM of 4 and 15 is 60.
Find the LCM of 6 and 14. D. 42
0% D
A B C 0% D C
0% B
A
0%
1. 2. 3. 4.
WORK On an assembly line, machine A must be oiled every 18 minutes, machine B every 24 minutes, and machine C every 48 minutes. If all three machines are turned on at the same time, in how many minutes will all three machines need to be oiled at the same time? First, find the LCM of 18, 24, and 48. 18 = 2 × 32 24 = 23 × 3 48 = 24 × 3 LCM: 24 × 32 = 144
Answer: So, all three machines will need to be oiled at the same time in 144 minutes.
LIGHTS Brenda put up three different strands of decorative blinking lights. The first strand blinks every 6 seconds while the second strand blinks every 8 seconds. The third strand blinks every 4 seconds. If all strands blink at the same time, in how many seconds will they again blink at the same time? D. 24 s 1. 2. 3. 4.
0% D
0% C
0% B
A
0%
A B C D
End of the Lesson
Homework – Pg 213, # 8-29 all
Five-Minute Check (over Lesson 4–7) Image Bank Math Tools
Percents Prime Factorization
(over Lesson 4-7)
Write 13.7% as a decimal. B. 0.137
0% D
A B C 0% D C
0% B
A
0%
1. 2. 3. 4.
(over Lesson 4-7)
D. 0.0725
0% D
A B C 0% D C
0% B
A
0%
1. 2. 3. 4.
(over Lesson 4-7)
Write 0.183 as a percent. B. 18.3%
0% D
A B C 0% D C
0% B
A
0%
1. 2. 3. 4.
(over Lesson 4-7)
Write 0.07 as a percent. C. 7%
0% D
A B C 0% D C
0% B
A
0%
1. 2. 3. 4.
(over Lesson 4-7)
Assuming every student placed a vote, if 0.83 of the student body voted for Afsheen and 0.17 voted for Neal, what percent of the student body voted for Neal? A. 17% A B C 0% D D
C
0% B
A
0%
1. 2. 3. 0% 4.
(over Lesson 4-7)
What is
% written as a decimal?
A. 0.32 B. 3.2 A B C 0% D
0% D
A
D. 0.325
0% B
0%
1. 2. 3. 4.
C
C.
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